Estimation and Inference of Treatment Effects Using a New Panel Data Approach: Measuring the Impact of US SYG Law

This paper proposes a new panel data approach to evaluate the impact of social policy. We consider a classical panel model with interactive ?xed e?ects (IFE), which allows the cross-sectional dependence through the presence of some (unobserved) common factors. The new approach combines the ideas of Pesaran (2006) to estimate the panel model with IFE and Hsiao et al. (2012) to construct counterfactuals. For the new approach, instead of estimating the unobserved factors, we propose to use the observed data. Compared to the existing methods such as Synthetic Control Method (SCM) (Abadie et al. (2010)) and the Generalized SCM (GSCM) (Xu (2017)), our new approach possesses the advantages of: (1) there is no need to impose constraints on both the observables and unobservables; (2) the number of parameters to be estimated in the model is greatly reduced. Moreover, we establish the asymptotic properties for the average treatment e?ect (ATE) over post-treatment periods, which can be used to obtain statistical inference for the signi?cance of ATE or to construct con?dence band for the treatment e?ects in the post-treatment periods. Monte Carlo simulations show that our approach works remarkably well and has very desirable ?nite sample performance in terms of estimation bias, mean square of errors, and empirical rejection frequency. We apply our method to study the impact of the US Stand Your Ground (SYG) law on the state-level murder rate, and we ?nd, in general, the SYG law has increased the murder rate for the states adopting the SYG law.